Name Date Class 9A Dear Family, A Family Letter: Understanding Integers The student will begin the study of an important set of numbers called integers. Integers are the set of numbers that include all positive and negative whole numbers. The student will learn how to graph integers on a number line. Name a positive or negative number to represent each situation. A. a gain of 2 points in the stock market Positive numbers can represent gains or increases. 2 B. a 15 yard penalty in football Negative numbers can represent losses or decreases. 15 The student will graph integers and their opposites on a number line. Opposites are two numbers that are an equal distance from zero on a number line. Graph the integer 6 and its opposite on a number line. 6 is the same distance from 0 as 6. Absolute value represents the distance from zero an integer is on a number line. The absolute value of a number is always positive because it reflects a distance, which is always a positive value. Therefore, opposites always have the same absolute value. Use the number line to find the absolute value of 3. 3 is 3 units from 0, so 3 3. Vocabulary These are the math words we are learning: absolute value an integer s distance from 0 on a number line; the symbol for absolute value is. coordinates the numbers in an ordered pair that locate a point on a coordinate plane integers the set of all whole numbers and their opposites negative number integer less than zero opposites two numbers that are an equal distance from zero on a number line origin the point where the x-axis and y-axis intersect on the coordinate plane positive number integer greater than zero quadrants the four areas created by the axes on a coordinate plane 9-1
9A A Family Letter: Understanding Integers continued The student will also learn to compare and order integers. It is important to remember that negative numbers are ALWAYS less than positive numbers. Use the number line to compare each pair of integers. Write or. 5 3 5 is to the left of 3 on the number line. 5 3 This is just the beginning of the student s involvement with integers. Understanding the concept of positive and negative values is important as the student continues in mathematics. Sincerely, 9-2
9A A At-Home Practice: Understanding Integers Name a positive or negative number to represent each situation. 1. a loss of 15 yards in football 2. an increase of 52 points Graph each integer and its opposite on a number line. 3. 10 4. 8 Use the number line to find the absolute value of each integer. 5. 4 6. 6 7. 9 Use the number line to compare each pair of integers. Write or. 8. 0 5 9. 3 5 10. 2 4 Order, the integers in each set from least to greatest. 11. 6, 2, 4 12. 0, 5, 7 13. 9, 8, 1, 1 Answers: 1. 15 2. 52 3. 4. 5. 4 6. 6, 7. 9 8. 9. 10. 11. 6, 4, 2 12. 7, 5, 0 13. 9, 1, 1, 8 9-3
9A A Family Fun: Integer Game Objective The objective is to collect all of the cards in the deck. Materials Deck of cards Directions Deal out the entire deck. Make sure the cards are face down. Every round is played the same way: each player turns over the top card in his or her hand. The player who has the card with the greatest value takes all the cards played that round. However Each black card holds a positive value with the aces being the least value and the kings being the greatest value. Each red card holds a negative value with the aces having the greatest value and the kings having the least value. For example: If a red 7 and a black 2 are turned over, the player with the black 2 will win that round because 2 7. If there is a tie or a round where two cards with the same value are played, each player deals out 3 cards face down. The last card dealt is turned over. The player with the card with the greatest value takes all the cards that round. The winner is the player who ends up with all the cards or who has the greatest number of cards at the end of the game. 9-4
Name Date Class 9B Dear Family, B Family Letter: Understanding Integers Now that the student has a basic understanding of integers, he or she will be introduced to the coordinate plane. The student will graph or name points in all four quadrants of the coordinate plane. Give the coordinates of point D. From the origin, D is three units to the right and 2 units down. (3, 2) Vocabulary These are the math words we are learning: axes the two number lines in a coordinate plane coordinates the numbers in an ordered pair that locate a point on a coordinate plane coordinate plane formed by two number lines in a plane that intersect at right angles at zero on each number line origin the point where the x-axis and y-axis intersect on the coordinate plane quadrants the four areas created by the axes on a coordinate plane x-axis the horizontal axis on the coordinate plane x-coordinate the first number in an ordered pair y-axis the vertical axis on the coordinate plane y-coordinate the second number in an ordered pair 9-21
9B B Family Letter: Understanding Integers continued When a polygon is graphed in the coordinate plane, the student can find the length of the sides of the polygon using the units of the grid for any sides that are parallel to either axes. In the graph below, the vertices of the polygon are at A( 3, 4), B(2, 4), C(2, 1) and D( 3, 1). A B D C Because segments AB and DC are horizontal lines (parallel to the x-axis and segments AD and BC are vertical lines (parallel to the y-axis), their lengths are found by counting the units. The length of AB is 5 units. The length of DC is 5 units. The length of AD is 5 units. The length of BC is 5 units. By knowing the lengths of the sides of the polygon graphed, the student can now classify the polygon as a square because all four sides have the same length. The student is also able to find the perimeter of the square by adding the lengths of the sides, 5 + 5 + 5+ 5 = 20. Square ABCD has a perimeter of 20 units. Sincerely, 9-22
9B B At-Home Practice: Understanding Integers Graph each set of vertices on a coordinate plane and answer the questions. 1. A polygon has vertices at (2, 0), (6, 0), (3, 6), and (6, 6). What type of polygon is this? What is its perimeter? 2. A polygon has vertices at ( 2, 2), (4, 2), ( 2, 4), and (4, 4). What type of polygon is this? What is its perimeter? Answers: 1. rectangle; 14 units 2. square; 24 units. 9-23
9B B Family Fun: Graphing the Living Room Use the coordinate plane to make a diagram of the living room in your house. Include a rectangle for a couch, a square for a chair, and either a rectangle or a square for any tables. After you have made a graph of the living room, have everyone in the house go to the living room and sit down. Now, mark the location of each person on your graph using an X and the name of the ordered pair. Label each ordered pair with a letter for that person s name. 9-24